Solution of differential equation dy – sin x sin y dx = 0 is :

$e^{\cos x} \tan \frac{y}{2}=c$

Given equation can be written as :

$\frac{d y}{\sin y}=\sin x d x$

$\Rightarrow \int cosec ~y~d y=\int \sin x~ d x+c$

$\Rightarrow \log \tan \frac{y}{2}=-\cos x+c_1$

$\Rightarrow \tan \frac{y}{2}=e^{-\cos x} . e^{c_1}$

$\Rightarrow e^{\cos x} . \tan \frac{y}{2}=c$

Hence (1) is the correct answer.